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Resources tagged with Number - generally similar to A Problem Is a Problem for All That...:

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Broad Topics > Numbers and the Number System > Number - generally

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Multiplication Magic

Stage: 4 Challenge Level: Challenge Level:1

Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .

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Add 3 Dice

Stage: 2, 3 and 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

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Factorial

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

How many zeros are there at the end of the number which is the product of first hundred positive integers?

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A Story about Absolutely Nothing

Stage: 2, 3, 4 and 5

This article for the young and old talks about the origins of our number system and the important role zero has to play in it.

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The Secret World of Codes and Code Breaking

Stage: 2, 3 and 4

When you think of spies and secret agents, you probably wouldn’t think of mathematics. Some of the most famous code breakers in history have been mathematicians.

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Black Box

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This black box reveals random values of some important, but unusual, mathematical functions. Can you deduce the purpose of the black box?

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Big and Small Numbers in Biology

Stage: 4 Challenge Level: Challenge Level:1

Work with numbers big and small to estimate and calulate various quantities in biological contexts.

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Find the Fake

Stage: 4 Challenge Level: Challenge Level:1

There are 12 identical looking coins, one of which is a fake. The counterfeit coin is of a different weight to the rest. What is the minimum number of weighings needed to locate the fake coin?

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Latin Numbers

Stage: 4 Challenge Level: Challenge Level:1

Let N be a six digit number with distinct digits. Find the number N given that the numbers N, 2N, 3N, 4N, 5N, 6N, when written underneath each other, form a latin square (that is each row and each. . . .

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N000ughty Thoughts

Stage: 4 Challenge Level: Challenge Level:1

Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .

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More Mods

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What is the units digit for the number 123^(456) ?

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Mod 3

Stage: 4 Challenge Level: Challenge Level:1

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

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Novemberish

Stage: 4 Challenge Level: Challenge Level:1

a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.

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Euler's Officers

Stage: 4 Challenge Level: Challenge Level:1

How many different solutions can you find to this problem? Arrange 25 officers, each having one of five different ranks a, b, c, d and e, and belonging to one of five different regiments p, q, r, s. . . .

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Squaresearch

Stage: 4 Challenge Level: Challenge Level:1

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

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Largest Product

Stage: 3 and 4 Challenge Level: Challenge Level:1

Which set of numbers that add to 10 have the largest product?